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A stochastic multiscale coupling scheme to account for sampling noise in atomistic-to-continuum simulations

Multiscale Modeling and Simulation

Salloum, Maher S.; Sargsyan, Khachik S.; Jones, Reese E.; Debusschere, Bert D.; Najm, H.N.; Adalsteinsson, Helgi A.

We present a methodology to assess the predictive fidelity of multiscale simulations by incorporating uncertainty in the information exchanged between the atomistic and continuum simulation components. Focusing on uncertainty due to finite sampling in molecular dynamics (MD) simulations, we present an iterative stochastic coupling algorithm that relies on Bayesian inference to build polynomial chaos expansions for the variables exchanged across the atomistic-continuum interface. We consider a simple Couette flow model where velocities are exchanged between the atomistic and continuum components. To alleviate the burden of running expensive MD simulations at every iteration, a surrogate model is constructed from which samples can be efficiently drawn as data for the Bayesian inference. Results show convergence of the coupling algorithm at a reasonable number of iterations. The uncertainty associated with the exchanged variables significantly depends on the amount of data sampled from the MD simulations and on the width of the time averaging window used in the MD simulations. Sequential Bayesian updating is also implemented in order to enhance the accuracy of the stochastic algorithm predictions. © 2012 Society for Industrial and Applied Mathematics.

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TYPE Journal Article YEAR 2012
OSTIScopus

Efficient uncertainty quantification methodologies for high-dimensional climate land models

Sargsyan, Khachik S.; Safta, Cosmin S.; Berry, Robert D.; Ray, Jaideep R.; Debusschere, Bert D.; Najm, H.N.

In this report, we proposed, examined and implemented approaches for performing efficient uncertainty quantification (UQ) in climate land models. Specifically, we applied Bayesian compressive sensing framework to a polynomial chaos spectral expansions, enhanced it with an iterative algorithm of basis reduction, and investigated the results on test models as well as on the community land model (CLM). Furthermore, we discussed construction of efficient quadrature rules for forward propagation of uncertainties from high-dimensional, constrained input space to output quantities of interest. The work lays grounds for efficient forward UQ for high-dimensional, strongly non-linear and computationally costly climate models. Moreover, to investigate parameter inference approaches, we have applied two variants of the Markov chain Monte Carlo (MCMC) method to a soil moisture dynamics submodel of the CLM. The evaluation of these algorithms gave us a good foundation for further building out the Bayesian calibration framework towards the goal of robust component-wise calibration.

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TYPE SAND Report YEAR 2011
DOIOSTI

Real-time characterization of partially observed epidemics using surrogate models

Safta, Cosmin S.; Ray, Jaideep R.; Sargsyan, Khachik S.; Lefantzi, Sophia L.

We present a statistical method, predicated on the use of surrogate models, for the 'real-time' characterization of partially observed epidemics. Observations consist of counts of symptomatic patients, diagnosed with the disease, that may be available in the early epoch of an ongoing outbreak. Characterization, in this context, refers to estimation of epidemiological parameters that can be used to provide short-term forecasts of the ongoing epidemic, as well as to provide gross information on the dynamics of the etiologic agent in the affected population e.g., the time-dependent infection rate. The characterization problem is formulated as a Bayesian inverse problem, and epidemiological parameters are estimated as distributions using a Markov chain Monte Carlo (MCMC) method, thus quantifying the uncertainty in the estimates. In some cases, the inverse problem can be computationally expensive, primarily due to the epidemic simulator used inside the inversion algorithm. We present a method, based on replacing the epidemiological model with computationally inexpensive surrogates, that can reduce the computational time to minutes, without a significant loss of accuracy. The surrogates are created by projecting the output of an epidemiological model on a set of polynomial chaos bases; thereafter, computations involving the surrogate model reduce to evaluations of a polynomial. We find that the epidemic characterizations obtained with the surrogate models is very close to that obtained with the original model. We also find that the number of projections required to construct a surrogate model is O(10)-O(10{sup 2}) less than the number of samples required by the MCMC to construct a stationary posterior distribution; thus, depending upon the epidemiological models in question, it may be possible to omit the offline creation and caching of surrogate models, prior to their use in an inverse problem. The technique is demonstrated on synthetic data as well as observations from the 1918 influenza pandemic collected at Camp Custer, Michigan.

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TYPE SAND Report YEAR 2011
DOIOSTI
Results 226–250 of 272
Results 226–250 of 272